FFTW 2.x builds a .la file (under fftw/.libs directory).
I think I need a .so file to link to. (I am not sure, because I am a gcc newbie).
In general on Linux, a .so file is dynamic library and a .a or .la is for statically linking with. Which one you need depends on your application and how you installed/built the library. For a tutorial on static vs. dynamic linking see this site. Also, did you build fftw yourself from source, or did you use a package manager? This would help answer your question. As for using gcc, check out this manual page, it might clear some stuff up.
So yeah, the short answer is either to stick with the .a or when building fftw specify that you want a shared library. ./configure --enable-shared